1. 1 Oldroyd B Model Bead formation in filament stretching Stretching phase Capillary thinning phase Connection between the bead and filament becomes unstable Thins to form a new thinner filament Fluid in middle retracts to form a bead Filament Stretching Srinivas Yarlanki, Oliver Harlen

2. 2 Particles suspended in polymeric fluids Ahamadi Malidi, Oliver Harlen Two-dimensional simulations of freely suspended particles in a polymeric fluid: Shear flow: Lee Edwards cell Planar Extensional flow: Kraynik-Reinelt cell In both cases: Biperiodic lattice to extend a unit cell containing N particles to an infinite domain.

3. 3 Steady State Shear - Dumbbell Models OldroydB and Fene-CR (L=5)  = 0.13 Viscosity First Normal Stress Difference Particles produce a shear-thickening fluid Simulation Boger Fluid Experiments (Scirocco, Vermant & Mewis JOR 2005) Increase in N 1

4. 4 Steady Shear – Pompom model  b.. Shear viscosity increases with particle volume fraction For low shear-rates N 1 increases with  but at higher shear-rates it decreases.

5. 5 Average Stress and Shear-rate in a Suspension Average stress Average shear-rate This suggests shift in viscosity shift in shear-rate Assume particle stress is proportional to fluid stress This seems to work for the pompom model! but not for Oldroyd or FENE models  .

6. 6 Transient case: Shifting model Shifting strain and stress for same effective shear-rate not only gives the steady state but the also transient !

7. 7 Average Velocity Gradient Why does shifting work for one model but not another? Simple shear is an equal balance between extension and rotation = + Particles are free to rotate but cannot strain extension rotation K = E +  is particle rotation Balance is changed to a flow with more extension than rotation.

8. 8 Particle Chaining Scirocco et al JNNFM 2004 Continuous shearing generates particle chaining in CMC solution But not in a Boger fluid

9. 9 Two-Particle Interactions: Oldroyd-B model vs Pompom No Alignment for Oldroyd-B (Boger Fluid) Particles align on same streamline – chaining Alignment for Pom-Pom model: Shear- thinning

10. 10 Planar “Extensional Viscosity” adding particles decreases extensional viscosity at higher strain-rates FENE –CR L=10 Pompom q=10

11. 11 20% glass filled LDPE J Embery solid pure squares filled time  Fillers suppress extension hardening Cross-over in extensional stress

12. 12 Conclusions Dumbbell models (Oldroyd B, FENE) shear-thicken. Pair tumbling Tube models (Pompom, RoliePoly) – suspension viscosity can be found from simple shift. Pair alignment – chaining? Qualitative experimental agreement In shear flow qualitatively different behaviour between dumbbell (Oldroyd, FENE) and tube theory based models (pompom Roliepoly). Planar extension In strain-hardening materials particles decrease the extensional viscosity. Real system is 3D and contains many particles Extensions Deformable particles, anisotropic particles, drops, bubbles etc…

13. 13 Pompom q=2,We s =0.5 Development of polymer stretch Elongated regions of more highly stretched polymer

14. 14 Effect of change of flow type Find  xy for the velocity gradient from rotation rate found in simulations for  Oldroyd B Dramatic increase in  xy  as  increases due to change in flow type. Fluid particles separate exponentially (rather than algebraically) coil-stretch transition Normal stresses grow even more!.  xy .

15. 15 Pompom model  xy .  xx –  yy ) .  Shifting shear-rate by  ..  xy . .. No great increase in stretch  Pompom model is not sensitive to change in flow type since dynamics is confined to a tube

16. 16 Transient case: removing the oscillation Aligned Initial Cond. Staggered Initial Cond. Superposition Average

17. 17 Multimode Roliepoly model Shear viscosity shifting works! normal stresses Presence of particles decreases normal stress difference for but increases it for

18. 18 20% Glass filled HDPE

19. 19 Planar Extensional Flow (Kraynik-Reneilt lattice) Square unit cell inclined at angle 0.55 radians to extensional axis Lattice replicates after Hencky strain  0.962 q p Each point (x,y) in unit cell has a infinite number of images (x,y) m,n located at